In Drosophila, Dichaete ( \(D\) ) is a mutation on chromosome III with a dominant effect on wing shape. It is lethal when homozygous. The genes \(e\)bony body \((e)\) and pink eye (p) are recessive mutations on chromosome III. Flies from a Dichaete stock were crossed to homozygous ebony, pink flies, and the \(\mathrm{F}_{1}\) progeny with a Dichaete phenotype were backcrossed to the ebony, pink homozygotes. (a) Using the results of this backcross shown in the following table, diagram the cross, showing the genotypes of the parents and offspring of both crosses. (b) What is the sequence and interlocus distance between these three genes?

The first stock flies are Dichaete \((D)\) crossed with homozygous ebony \((ee)\) and pink \((pp)\) flies. Since Dichaete \((D)\) is dominant and lethal when homozygous, these flies must be heterozygous for the Dichaete gene, having \((Dd)\) genotype. The genotypes of the parent flies are \((DdEePp)\) and \((ddeepp)\).

In the first generation, the progeny with a Dichaete phenotype are selected for and backcrossed to the ebony, pink homozygotes (having \((ddeepp)\) genotype). Since Dichaete \((D)\) is dominant and only these flies are backcrossed, the genotype must be \((D_EePp)\).

Using the backcross offspring results given in the table, we can calculate the recombination frequencies between ebony \((e)\) and Dichaete \((D)\), and Dichaete \((D)\) and pink \((p)\). Recombination frequency is equal to the sum of recombinant offspring divided by the total offspring. For example, the recombination frequency between ebony \((e)\) and Dichaete \((D)\) is the sum of ebony \((e)\) and Dichaete \((D)\) recombinant offspring divided by the total number of offspring. Let's denote the given number of offspring with each phenotype as follows: 1. \(N_{DEP}\) - Number of Dichaete, ebony, pink offspring 2. \(N_{Dep}\) - Number of Dichaete, ebony, non-pink offspring 3. \(N_{deP}\) - Number of non-Dichaete, ebony, pink offspring 4. \(N_{dep}\) - Number of non-Dichaete, ebony, non-pink offspring Then, based on the table provided, we calculate the recombination frequencies: Recombination frequency between ebony \((e)\) and Dichaete \((D)\): \(\frac{N_{Dep} + N_{deP}}{N_{DEP} + N_{Dep} + N_{deP} + N_{dep}}\) Recombination frequency between Dichaete \((D)\) and pink \((p)\): \(\frac{N_{DEP} + N_{deP}}{N_{DEP} + N_{Dep} + N_{deP} + N_{dep}}\)

To determine the sequence and distance between the three genes, we first find the order of the genes. Since the recombination frequencies are known, the lowest recombination frequency corresponds to genes that are closest together. In this case, we use the recombination frequencies to arrange genes in ascending order. Next, we calculate the interlocus distance between the genes by multiplying the recombination frequency by 100 (since 1% recombination frequency corresponds to 1 map unit, or centimorgan (cM)). We can then use this map distance to get the sequence and interlocus distance between the three genes.